Thanks for your patience but this is still confusing. It's clear from your explanation that the moves and end-game states are given at the start of learning (now that you mention it, I remember the bit about illegal actions leading to a game loss). So training does not start from scratch without knowing anything about the game. The system knows what moves are _legal_ (not just possible) and it knows when the game ends, and how to score it. I don't see how this supports the claim of "no rules".

I appreciate that someone explaiend this to you at some point but I'm going with what I've read in some of the published papers and the ones I've read really leave a lot to the imagination. That is no way to present and support such big claims as "no rules", "no hands", especially when this is the central claim in a paper. Why fudge this so much when it's such an important aspect of the whole contribution? [1] You (general you) make a claim? Support the claim.

I didn't get what you mean about logic programming? Where does that come in?

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[1] Oh, I know why. It's the whole silly game with machine learning publications where they never tell you everything and you have to figure it out yourself. Well I like to play the other game, where I call bullshit unless it's explained clearly. In the paper. Not on Twitter and not by kind colleagues.

Silly games don't advance the science though.

>> Of course DM has a chess function which does codes the rules of the next move. It can return a LOSS if you try an illegal move. But this function is NOT called for the tree roll out.

I see what you mean- the chess function computes the results of actions returned by the system. But, if you do rollouts you need to have a set of actions from which to choose and an internal representation of states resulting from those actions. MuZero learns to predict those actions and states- but that means it selects from sets of possible actions and states. The paper does not explain where do these sets come from.

For ATARI I get it, there's the physical ish controls and video frames. For the board games however, I remember very clearly from the AlphaZero paper that there was an encoding of "knight moves" and "queen moves". I also remember less clearly that the structure of the network's layers mirrored the layout of a chessboard. That's what I mean by hard-coding and in the MuZero paper there are many references to reusing the AlphaZero archietecture and no explanation of how the same components (board states, moves) are represented in MuZero.